Theorem dral2 1966

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)

Hypothesis

Ref	Expression
dral1.1	⊢ (∀x x = y → (φ ↔ ψ))

Assertion

Ref	Expression
dral2	⊢ (∀x x = y → (∀zφ ↔ ∀zψ))

Proof of Theorem dral2

Step	Hyp	Ref	Expression
1		hbae 1953	. 2 ⊢ (∀x x = y → ∀z∀x x = y)
2		dral1.1	. 2 ⊢ (∀x x = y → (φ ↔ ψ))
3	1, 2	albidh 1590	1 ⊢ (∀x x = y → (∀zφ ↔ ∀zψ))

Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  drnf2  1970  equveli  1988  sbal1  2126  drnfc1  2505  drnfc2  2506